Plotting the results of Utility Values¶

!pip install plotly
import math
import random

import numpy as np
import pandas as pd
import plotly.express as px
import plotly.graph_objects as go

Requirement already satisfied: plotly in /home/wtt/anaconda3/lib/python3.7/site-packages (4.5.4)
Requirement already satisfied: retrying>=1.3.3 in /home/wtt/anaconda3/lib/python3.7/site-packages (from plotly) (1.3.3)
Requirement already satisfied: six in /home/wtt/anaconda3/lib/python3.7/site-packages (from plotly) (1.13.0)

Reading csv¶

DF_original_VI = pd.read_csv("results/original_value_iteration_utility_history.csv", header=None).transpose()
DF_original_PI = pd.read_csv("results/original_modified_policy_iteration_utility_history.csv", header=None).transpose()

DF_expt1_VI = pd.read_csv("results/experiment1_value_iteration_utility_history.csv", header=None).transpose()
DF_expt1_PI = pd.read_csv("results/experiment1_modified_policy_iteration_utility_history.csv", header=None).transpose()

DF_expt2_VI = pd.read_csv("results/experiment2_value_iteration_utility_history.csv", header=None).transpose()
DF_expt2_PI = pd.read_csv("results/experiment2_modified_policy_iteration_utility_history.csv", header=None).transpose()

# index : (Description, DataFrame, color_of_graph, scale)
DF_dict = {0 : ("DF-Original (Value Iteration) - 36 States", DF_original_VI, "darkred", 1), 
           1 : ("DF-Original (Policy Iteration) - 36 States", DF_original_PI, "red", 1), 
           2 : ("DF-Experiment1 (Value Iteration) - 144 States", DF_expt1_VI, "darkgreen", 2),
           3 : ("DF-Experiment1 (Policy Iteration) - 144 States", DF_expt1_PI, "limegreen", 2),
           4 : ("DF-Experiment2 (Value Iteration) - 324 States", DF_expt2_VI, "darkblue", 3),
           5 : ("DF-Experiment2 (Policy Iteration) - 324 States", DF_expt2_PI, "skyblue", 3),}

Display DF¶

for i, (k, v) in enumerate(DF_dict.items()):
    print("\n> " + v[0] + ":")
    display(v[1])

> DF-Original (Value Iteration) - 36 States:

> DF-Original (Policy Iteration) - 36 States:

> DF-Experiment1 (Value Iteration) - 144 States:

> DF-Experiment1 (Policy Iteration) - 144 States:

> DF-Experiment2 (Value Iteration) - 324 States:

> DF-Experiment2 (Policy Iteration) - 324 States:

Sorted States according to utility values¶

Highest Utility to Lowest Utility States

For Experiment1 & Experiment 2, the states have been scaled down to represent the states in the scaled-down version.

for i, (k, v) in enumerate(DF_dict.items()):
    print(v[0], ":", v[1].shape)
    temp_df = pd.DataFrame(v[1].iloc[-1, :])
    temp_df = temp_df.sort_values(temp_df.columns[0], ascending=False)
    temp_df = [int(element/(v[3]**2)) for element in temp_df.index]
    print(temp_df, "\n")

DF-Original (Value Iteration) - 36 States : (689, 36)
[0, 1, 2, 7, 8, 3, 12, 13, 9, 19, 4, 18, 30, 14, 15, 20, 26, 5, 24, 33, 27, 32, 11, 21, 31, 34, 17, 28, 23, 35, 29, 10, 25, 22, 6, 16] 

DF-Original (Policy Iteration) - 36 States : (8, 36)
[0, 1, 2, 7, 8, 3, 12, 13, 9, 19, 4, 18, 30, 14, 15, 20, 26, 5, 24, 33, 27, 32, 11, 21, 31, 34, 17, 28, 23, 35, 29, 10, 25, 22, 6, 16] 

DF-Experiment1 (Value Iteration) - 144 States : (689, 144)
[0, 0, 3, 3, 12, 33, 15, 12, 30, 33, 15, 30, 21, 21, 18, 18, 0, 28, 25, 34, 34, 18, 27, 18, 28, 15, 31, 27, 25, 3, 31, 12, 22, 21, 15, 0, 33, 21, 31, 19, 34, 28, 24, 35, 30, 24, 31, 22, 25, 3, 28, 32, 12, 34, 1, 35, 19, 6, 9, 4, 25, 32, 16, 33, 30, 1, 22, 35, 6, 29, 9, 13, 4, 7, 32, 16, 19, 1, 10, 35, 22, 26, 29, 7, 4, 32, 29, 16, 10, 1, 13, 7, 29, 4, 26, 19, 26, 10, 13, 16, 2, 7, 26, 5, 23, 10, 13, 2, 23, 5, 20, 2, 20, 5, 17, 17, 2, 5, 8, 14, 14, 8, 11, 11, 11, 6, 6, 8, 8, 24, 9, 9, 11, 23, 20, 14, 14, 27, 17, 17, 24, 23, 20, 27] 

DF-Experiment1 (Policy Iteration) - 144 States : (13, 144)
[0, 3, 3, 0, 12, 15, 12, 33, 30, 33, 15, 30, 21, 21, 18, 18, 0, 18, 18, 27, 15, 28, 25, 3, 27, 28, 34, 34, 25, 12, 31, 31, 22, 21, 15, 21, 0, 19, 33, 24, 30, 31, 28, 24, 34, 35, 31, 3, 22, 25, 12, 28, 32, 1, 34, 19, 6, 35, 9, 4, 25, 32, 16, 33, 30, 1, 22, 6, 35, 9, 29, 13, 4, 7, 32, 16, 19, 1, 10, 22, 26, 35, 7, 4, 29, 32, 29, 16, 10, 1, 13, 7, 4, 29, 19, 26, 10, 13, 16, 26, 2, 7, 5, 26, 10, 13, 23, 2, 5, 23, 20, 2, 20, 5, 17, 2, 17, 5, 8, 14, 14, 8, 11, 11, 8, 8, 9, 6, 6, 14, 9, 11, 11, 14, 27, 27, 17, 17, 24, 24, 23, 23, 20, 20] 

DF-Experiment2 (Value Iteration) - 324 States : (689, 324)
[0, 2, 0, 0, 4, 4, 4, 2, 2, 12, 14, 12, 34, 34, 32, 14, 12, 16, 32, 30, 34, 16, 14, 32, 30, 22, 26, 35, 22, 28, 35, 22, 35, 24, 20, 26, 33, 20, 28, 33, 20, 24, 33, 18, 26, 31, 16, 30, 18, 28, 31, 18, 24, 31, 22, 0, 18, 18, 28, 16, 18, 2, 28, 30, 34, 29, 35, 14, 32, 20, 30, 20, 22, 33, 16, 29, 27, 28, 22, 4, 12, 30, 18, 22, 31, 16, 25, 29, 20, 32, 34, 32, 14, 20, 26, 0, 20, 34, 27, 26, 35, 30, 2, 26, 33, 22, 24, 12, 4, 32, 14, 18, 20, 25, 27, 31, 22, 24, 34, 24, 0, 35, 2, 33, 16, 23, 29, 6, 10, 30, 12, 4, 25, 18, 31, 34, 32, 30, 0, 35, 2, 33, 32, 10, 6, 14, 23, 27, 16, 21, 29, 4, 31, 34, 0, 35, 2, 33, 8, 6, 23, 25, 10, 12, 29, 19, 16, 4, 6, 31, 29, 0, 35, 2, 33, 14, 21, 27, 8, 10, 17, 6, 4, 29, 31, 8, 27, 1, 3, 8, 21, 25, 12, 27, 10, 14, 19, 15, 17, 6, 8, 29, 5, 27, 1, 25, 3, 10, 8, 27, 7, 15, 25, 13, 17, 5, 25, 12, 1, 19, 23, 3, 11, 9, 25, 7, 13, 15, 23, 5, 1, 21, 11, 3, 9, 23, 13, 7, 5, 21, 1, 11, 9, 19, 21, 3, 5, 19, 1, 19, 3, 17, 5, 17, 1, 17, 3, 15, 5, 15, 15, 1, 3, 13, 13, 5, 7, 13, 1, 3, 11, 11, 7, 5, 9, 11, 9, 7, 9, 23, 23, 23, 15, 15, 28, 8, 19, 8, 24, 8, 7, 7, 7, 21, 17, 19, 15, 24, 24, 9, 28, 13, 13, 13, 19, 17, 6, 6, 11, 11, 11, 6, 26, 26, 26, 10, 10, 10, 17, 21, 28, 9, 9, 21] 

DF-Experiment2 (Policy Iteration) - 324 States : (15, 324)
[12, 12, 14, 14, 12, 16, 14, 16, 2, 0, 4, 4, 4, 2, 2, 0, 0, 34, 32, 34, 32, 34, 30, 22, 22, 22, 20, 30, 32, 20, 20, 18, 35, 35, 16, 35, 33, 33, 33, 26, 28, 24, 26, 31, 28, 24, 26, 18, 30, 31, 18, 28, 31, 24, 22, 18, 18, 16, 18, 14, 0, 2, 28, 20, 28, 34, 20, 30, 35, 29, 32, 16, 33, 30, 22, 29, 28, 27, 22, 12, 4, 30, 18, 16, 31, 29, 22, 25, 20, 14, 20, 34, 32, 32, 0, 20, 26, 26, 2, 34, 27, 30, 35, 26, 33, 22, 24, 12, 4, 32, 14, 18, 27, 31, 20, 25, 22, 24, 34, 0, 24, 35, 2, 33, 16, 10, 29, 23, 6, 30, 12, 4, 18, 25, 31, 34, 32, 30, 0, 35, 2, 33, 10, 6, 32, 14, 16, 27, 29, 23, 21, 4, 31, 34, 0, 35, 2, 33, 8, 10, 12, 6, 25, 23, 16, 19, 29, 4, 6, 31, 29, 0, 35, 2, 8, 14, 33, 10, 27, 21, 17, 6, 4, 29, 8, 31, 27, 1, 8, 3, 12, 25, 21, 10, 27, 14, 19, 6, 15, 17, 8, 29, 5, 27, 1, 25, 3, 10, 8, 27, 7, 15, 5, 13, 17, 25, 12, 1, 25, 19, 23, 3, 11, 9, 25, 7, 13, 15, 5, 23, 1, 11, 21, 3, 9, 23, 13, 7, 5, 21, 1, 11, 9, 3, 19, 21, 5, 19, 1, 19, 3, 17, 5, 17, 1, 17, 3, 15, 5, 15, 1, 15, 3, 13, 5, 13, 7, 13, 1, 3, 11, 7, 11, 5, 9, 11, 9, 7, 9, 7, 17, 9, 23, 19, 23, 17, 17, 19, 21, 7, 8, 8, 8, 19, 23, 21, 21, 7, 9, 13, 24, 24, 13, 28, 6, 6, 11, 11, 11, 28, 28, 26, 26, 26, 10, 15, 15, 15, 24, 10, 10, 13, 9, 6]

Graphs - Number of Iterations against Utility of State¶

for i, (k, v) in enumerate(DF_dict.items()):
    fig = go.Figure()
    for state_no in v[1].columns:
        fig.add_trace(go.Scatter(
            name="State " + str(state_no),
            x=v[1].index,
            y=v[1][state_no],
            mode="lines",
            showlegend=True))
    fig.update_layout(title={'text': v[0],
                             'y':0.9,
                             'x':0.45,
                             'xanchor': 'center',
                             'yanchor': 'top'},
                      xaxis_title="Iterations",
                      yaxis_title="Utility of State")
    fig.show()

Graph with Log-x Scale¶

for i, (k, v) in enumerate(DF_dict.items()):
    fig = go.Figure()
    for state_no in v[1].columns:
        fig.add_trace(go.Scatter(
            name="State " + str(state_no),
            x=v[1].index,
            y=v[1][state_no],
            mode="lines",
            showlegend=True))
    fig.update_layout(xaxis_type="log",
                      title={'text': v[0],
                             'y':0.9,
                             'x':0.45,
                             'xanchor': 'center',
                             'yanchor': 'top'},
                      xaxis_title="Iterations",
                      yaxis_title="Utility of State")
    fig.show()

	0	1	2	3	4	5	6	7	8	9	...	26	27	28	29	30	31	32	33	34	35
0	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0	0.0000	0.0000	0.0000	...	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000
1	1.0000	-0.0400	-0.0400	-0.0400	-0.0400	-0.0400	0.0	-1.0000	-0.0400	-0.0400	...	1.0000	-0.0400	-1.0000	-0.0400	1.0000	-1.0000	-0.0400	1.0000	-0.0400	-0.0400
2	1.9900	0.6490	-0.0790	-0.0790	-0.0790	-0.0790	0.0	-1.0390	-0.1740	-0.0790	...	1.7841	0.7520	-1.0390	-0.0790	1.8870	-0.4060	0.8470	1.7841	0.6490	-0.0790
3	2.9701	1.4974	0.4489	-0.1180	-0.1180	-0.1180	0.0	-0.5240	-0.2130	-0.1280	...	2.5713	1.4467	-0.4190	-0.1180	2.7550	0.4141	1.6335	2.5611	1.3343	0.4583
4	3.9404	2.4086	1.1692	0.2911	-0.1570	-0.1570	0.0	0.1373	0.2509	-0.1680	...	3.3414	2.2156	0.2364	0.2697	3.6133	1.2640	2.4047	3.3222	2.0790	1.0504
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
684	99.8966	98.2900	96.8451	95.4505	94.2091	92.8341	0.0	95.7796	95.4830	94.3491	...	92.9990	91.7110	89.4450	88.4657	93.2251	90.8145	91.6915	91.7847	90.4634	89.1943
685	99.8976	98.2910	96.8461	95.4515	94.2102	92.8351	0.0	95.7807	95.4841	94.3501	...	93.0000	91.7121	89.4461	88.4667	93.2261	90.8156	91.6925	91.7857	90.4644	89.1953
686	99.8987	98.2920	96.8472	95.4525	94.2112	92.8361	0.0	95.7817	95.4851	94.3512	...	93.0010	91.7131	89.4471	88.4678	93.2272	90.8166	91.6935	91.7868	90.4654	89.1964
687	99.8997	98.2930	96.8482	95.4535	94.2122	92.8372	0.0	95.7827	95.4861	94.3522	...	93.0021	91.7141	89.4481	88.4688	93.2282	90.8176	91.6946	91.7878	90.4664	89.1974
688	99.9007	98.2940	96.8492	95.4545	94.2132	92.8382	0.0	95.7837	95.4871	94.3532	...	93.0031	91.7151	89.4491	88.4698	93.2292	90.8186	91.6956	91.7888	90.4675	89.1984

	0	1	2	3	4	5	7	8	9	...	26	27	28	29	30	31	32	33	34	35
0	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	...	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000
1	19.9980	16.7777	2.4854	-1.1770	-1.1070	-1.0760	-2.3740	1.3982	-1.7760	...	6.8278	-1.8370	-0.8090	-1.0200	14.5490	4.3732	6.9548	12.5990	10.8006	9.2090
2	40.8225	39.2157	37.7693	36.3609	20.7942	21.7219	36.7038	36.3948	35.1479	...	28.2738	27.8182	25.8010	25.6718	33.4780	31.1267	28.0398	29.0297	27.7681	26.6449
3	56.2264	54.6198	53.1749	51.7802	50.5389	38.3277	52.1094	51.8128	50.6789	...	47.6995	43.8119	41.7008	41.1142	47.8191	45.4679	44.7084	44.7252	43.3863	42.1435
4	67.6206	66.0140	64.5691	63.1745	61.9332	59.6968	63.5037	63.2071	62.0731	...	59.7381	58.5331	56.2609	54.8723	58.4273	56.0760	58.2864	58.4196	57.1325	55.8486
5	76.0490	74.4423	72.9975	71.6028	70.3615	68.9865	71.9320	71.6354	70.5015	...	69.1404	67.8345	65.5546	64.3483	69.1860	66.7539	67.7952	67.7763	66.4682	65.1857
6	82.2834	80.6768	79.2319	77.8373	76.5959	75.2209	78.1664	77.8698	76.7359	...	75.3854	74.0972	71.8310	70.6358	75.6014	73.1895	74.0764	74.1696	72.8482	71.5553
7	86.8950	85.2884	83.8435	82.4489	81.2076	79.8325	82.7781	82.4815	81.3475	...	79.9974	78.7094	76.4434	75.4641	80.2230	77.8124	78.6898	78.7830	77.4617	76.1926

	0	1	2	3	4	5	6	7	8	9	...	134	135	136	137	138	139	140	141	142	143
0	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	...	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.000
1	1.0000	1.0000	-0.0400	-0.0400	-0.0400	-0.0400	-0.0400	-0.0400	-0.0400	-0.0400	...	-1.0000	-1.0000	-0.0400	-0.0400	1.0000	1.0000	-0.0400	-0.0400	-0.0400	-0.040
2	1.9900	1.9900	0.7441	-0.0790	-0.0790	-0.0790	-0.0790	-0.0790	-0.0790	-0.0790	...	-0.4060	-1.2290	-0.0790	0.7441	1.9900	1.9900	0.7441	-0.0790	-0.0790	-0.079
3	2.9701	2.9701	1.6740	0.5336	-0.1180	-0.1180	-0.1180	-0.1180	-0.1180	-0.1180	...	0.4957	-1.3060	0.6057	1.6936	2.9599	2.9599	1.6740	0.5336	-0.1180	-0.118
4	3.9404	3.9404	2.6254	1.3737	0.3590	-0.1570	-0.1570	-0.1570	-0.1570	-0.1570	...	1.4343	-0.7210	1.5096	2.6417	3.9191	3.9172	2.6101	1.3737	0.3590	-0.157
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
684	99.8966	99.8966	98.5678	97.2335	95.9107	94.6021	93.3096	92.0342	90.7874	89.5661	...	97.2254	94.7542	96.0280	97.1778	98.4549	98.4526	97.1294	95.8038	94.4919	93.197
685	99.8976	99.8976	98.5688	97.2345	95.9117	94.6031	93.3106	92.0352	90.7884	89.5672	...	97.2264	94.7552	96.0290	97.1788	98.4559	98.4536	97.1304	95.8048	94.4929	93.198
686	99.8987	99.8987	98.5698	97.2355	95.9127	94.6042	93.3116	92.0363	90.7895	89.5682	...	97.2274	94.7562	96.0300	97.1798	98.4569	98.4546	97.1314	95.8058	94.4939	93.199
687	99.8997	99.8997	98.5708	97.2365	95.9137	94.6052	93.3126	92.0373	90.7905	89.5692	...	97.2284	94.7572	96.0310	97.1808	98.4579	98.4556	97.1324	95.8068	94.4949	93.200
688	99.9007	99.9007	98.5718	97.2375	95.9147	94.6062	93.3136	92.0383	90.7915	89.5702	...	97.2294	94.7582	96.0320	97.1818	98.4589	98.4566	97.1334	95.8078	94.4959	93.201

	0	1	2	3	4	5	6	7	8	9	...	134	135	136	137	138	139	140	141	142	143
0	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	...	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000
1	14.7683	1.6568	-1.2520	-1.5980	-1.6350	-1.2810	-1.1300	-1.0750	-1.0540	-1.0450	...	3.5415	1.8936	1.5329	-1.0820	-3.3410	-5.3220	-6.7900	-2.5230	-1.9680	-1.4720
2	37.2340	37.2340	35.9032	34.4378	1.7332	-1.4330	-1.7760	-1.8120	-1.8110	-1.8110	...	34.1527	31.6736	30.0807	28.6277	27.0748	27.1675	0.9185	-1.6900	-1.9470	-2.0130
3	53.5725	53.5725	52.2425	50.8980	49.5533	48.2176	46.8954	45.5897	-2.3810	-2.3810	...	50.5546	48.0756	46.8338	45.5156	45.6116	45.6977	44.4619	43.2140	41.5690	6.5525
4	65.6576	65.6576	64.3287	62.9944	61.6715	60.3625	59.0681	57.7902	56.5414	29.7976	...	62.7456	60.2744	59.0836	58.2704	59.7960	59.7821	58.4718	57.1677	55.8753	54.5946
5	74.5969	74.5969	73.2680	71.9337	70.6110	69.3029	68.0115	66.7362	65.4894	64.2682	...	71.7475	69.2763	68.3839	69.8866	70.8273	70.7591	69.4033	68.0602	66.7333	65.4248
6	81.2093	81.2093	79.8805	78.5462	77.2234	75.9152	74.6235	73.3494	72.1036	70.8832	...	78.4063	75.9351	76.5689	76.8100	77.8928	77.9250	76.6374	75.3397	74.0531	72.7815
7	86.1005	86.1005	84.7717	83.4374	82.1146	80.8063	79.5144	78.2400	76.9939	75.7732	...	83.3317	80.8605	81.5439	81.8269	83.2183	83.2139	81.8959	80.5776	79.2742	77.9886
8	89.7185	89.7185	88.3897	87.0554	85.7326	84.4243	83.1322	81.8575	80.6112	79.3904	...	86.9751	84.5039	85.2845	86.1000	87.3080	87.3020	85.9751	84.6460	83.3306	82.0321
9	92.3948	92.3948	91.0660	89.7317	88.4089	87.1005	85.8083	84.5334	83.2870	82.0661	...	89.6701	87.1989	88.0357	89.0712	90.3045	90.2999	88.9751	87.6479	86.3341	85.0371
10	94.3744	94.3744	93.0456	91.7113	90.3885	89.0800	87.7878	86.5128	85.2663	84.0452	...	91.6636	89.1924	90.0696	91.2466	92.4960	92.4922	91.1681	89.8415	88.5284	87.2321
11	95.8388	95.8388	94.5099	93.1756	91.8528	90.5443	89.2520	87.9769	86.7303	85.5092	...	93.1382	90.6670	91.7108	92.8412	94.1010	94.0977	92.7739	91.4477	90.1351	88.8394
12	96.9219	96.9219	95.5931	94.2588	92.9360	91.6275	90.3351	89.0599	87.8133	86.5922	...	94.2290	91.7578	92.8743	94.0114	95.2779	95.2750	93.9514	92.6254	91.3131	90.0177

	0	1	2	3	4	5	6	7	8	9	...	314	315	316	317	318	319	320	321	322	323
0	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	...	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000
1	1.0000	1.0000	1.0000	-0.0400	-0.0400	-0.0400	-0.0400	-0.0400	-0.0400	-0.0400	...	-0.0400	1.0000	1.0000	1.0000	-0.0400	-0.0400	-0.0400	-0.0400	-0.0400	-0.0400
2	1.9900	1.9900	1.9900	0.7441	-0.0790	-0.0790	-0.0790	-0.0790	-0.0790	-0.0790	...	0.7441	1.9900	1.9900	1.9900	0.7441	-0.0790	-0.0790	-0.0790	-0.0790	-0.0790
3	2.9701	2.9701	2.9701	1.6834	0.5336	-0.1180	-0.1180	-0.1180	-0.1180	-0.1180	...	1.6834	2.9701	2.9701	2.9701	1.6834	0.5336	-0.1180	-0.1180	-0.1180	-0.1180
4	3.9404	3.9404	3.9404	2.6447	1.3989	0.3590	-0.1570	-0.1570	-0.1570	-0.1570	...	2.6466	3.9394	3.9404	3.9394	2.6447	1.3989	0.3590	-0.1570	-0.1570	-0.1570
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
684	99.8966	99.8966	99.8966	98.5966	97.3079	96.0296	94.7625	93.5073	92.2647	91.0353	...	98.5631	99.8608	99.8623	99.8603	98.5575	97.2656	95.9841	94.7138	93.4557	92.2105
685	99.8976	99.8976	99.8976	98.5977	97.3090	96.0306	94.7635	93.5083	92.2658	91.0363	...	98.5642	99.8619	99.8633	99.8613	98.5586	97.2667	95.9851	94.7148	93.4567	92.2115
686	99.8987	99.8987	99.8987	98.5987	97.3100	96.0317	94.7645	93.5094	92.2668	91.0373	...	98.5652	99.8629	99.8644	99.8624	98.5596	97.2677	95.9861	94.7158	93.4577	92.2125
687	99.8997	99.8997	99.8997	98.5997	97.3110	96.0327	94.7656	93.5104	92.2678	91.0384	...	98.5662	99.8639	99.8654	99.8634	98.5606	97.2687	95.9871	94.7169	93.4587	92.2135
688	99.9007	99.9007	99.9007	98.6007	97.3120	96.0337	94.7666	93.5114	92.2688	91.0394	...	98.5672	99.8649	99.8664	99.8644	98.5616	97.2697	95.9881	94.7179	93.4597	92.2145

	0	1	2	3	4	5	6	7	8	9	...	314	315	316	317	318	319	320	321	322	323
0	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	...	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000
1	21.0312	5.6499	2.7404	-0.0500	-0.7490	-0.7950	-1.2070	-2.4240	-2.5020	-2.4190	...	18.8126	21.1678	20.8203	21.1072	13.0664	11.8792	10.8249	4.2025	1.6768	2.0744
2	41.9960	41.9960	41.9960	40.5319	39.1264	37.7106	36.2779	34.5494	-1.4460	-1.8140	...	37.9847	39.3949	40.0966	40.1640	38.9226	37.6874	36.2060	34.7238	30.1129	28.7734
3	57.0983	57.0983	57.0983	55.7984	54.5095	53.2300	51.9595	50.6985	49.4477	48.2083	...	54.2811	55.5824	55.5821	55.5826	54.2811	52.9931	51.7139	50.3389	49.0065	47.7118
4	68.2656	68.2656	68.2656	66.9657	65.6769	64.3986	63.1315	61.8763	60.6336	59.4039	...	65.8326	67.1320	67.1337	67.1317	65.8289	64.5370	63.2555	61.9852	60.7270	59.4817
5	76.5261	76.5261	76.5261	75.2261	73.9374	72.6591	71.3920	70.1368	68.8942	67.6648	...	74.3786	75.6778	75.6795	75.6775	74.3747	73.0828	71.8012	70.5309	69.2728	68.0276
6	82.6363	82.6363	82.6363	81.3363	80.0476	78.7693	77.5022	76.2470	75.0044	73.7750	...	80.7014	81.9995	82.0010	81.9990	80.6962	79.4043	78.1227	76.8524	75.5943	74.3491
7	87.1561	87.1561	87.1561	85.8561	84.5674	83.2891	82.0220	80.7668	79.5242	78.2948	...	85.3776	86.6756	86.6771	86.6751	85.3723	84.0804	82.7989	81.5286	80.2704	79.0253
8	90.4994	90.4994	90.4994	89.1994	87.9107	86.6324	85.3652	84.1101	82.8675	81.6381	...	88.8366	90.1345	90.1360	90.1340	88.8312	87.5394	86.2578	84.9875	83.7294	82.4842
9	92.9724	92.9724	92.9724	91.6724	90.3837	89.1054	87.8382	86.5831	85.3405	84.1111	...	91.3953	92.6931	92.6946	92.6926	91.3898	90.0980	88.8164	87.5461	86.2880	85.0428
10	94.8017	94.8017	94.8017	93.5017	92.2130	90.9347	89.6675	88.4124	87.1698	85.9403	...	93.2880	94.5858	94.5872	94.5853	93.2825	91.9906	90.7090	89.4387	88.1806	86.9354
11	96.1548	96.1548	96.1548	94.8548	93.5661	92.2878	91.0207	89.7655	88.5229	87.2935	...	94.6880	95.9857	95.9872	95.9852	94.6824	93.3905	92.1090	90.8387	89.5806	88.3354
12	97.1557	97.1557	97.1557	95.8557	94.5670	93.2887	92.0216	90.7664	89.5238	88.2944	...	95.7236	97.0213	97.0228	97.0208	95.7180	94.4261	93.1445	91.8743	90.6161	89.3709
13	97.8961	97.8961	97.8961	96.5961	95.3074	94.0291	92.7619	91.5068	90.2642	89.0347	...	96.4896	97.7873	97.7888	97.7868	96.4840	95.1921	93.9106	92.6403	91.3821	90.1370
14	98.4437	98.4437	98.4437	97.1437	95.8550	94.5767	93.3096	92.0544	90.8118	89.5824	...	97.0562	98.3539	98.3554	98.3534	97.0506	95.7588	94.4772	93.2069	91.9488	90.7036